FIELD-THEORETIC METHODS FOR SEPARATED-PAIR BCS FUNCTIONS
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Date
1984
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Ohio State University
Abstract
The motivation for this work arose in large part from the belief that the intuitive ideas of A. C. $Wahl,^{1}$ originally expressed as ODC functions shortly after his accurate calculations of the Hartree-Fock wave function of $F_{2},^{2}$ could be combined with the methods of superconductivity theory. We have now derived a formalism which applies to BCS functions which have the proper symmetries of the problem and whose particle fluctuations are rigorously compensated. This is accomplished by a generalization of Lipkin's model-Hamiltonian $method^{3}$ for wave packets that gives as zeroth-order a separated-pair theory. Since our zeroth-order function is a BCS function, we are able to define the contributions of higher-orders rigorously using essentially ordinary Feynman diagrams and rules for their evaluation. After carrying out systematic orbital and operator $transformations,^{4}$ the perturbation theory becomes even simpler than its forebear proposed by $Numbu.^{5}$ This transpires because we are able to derive charge distributions that accommodate the new l-particle states and their fractional occupancies simultaneously, and because the $2 \times 2$ propagator matrices become essentially idempotent. At present, we have explicit expressions for all diagrams through third order which arise from the 2-body Lipkin Hamiltonian. In the (unlikely) event that we will have calculations completed for $F_{2}$ before this symposium, these will be described.
Description
$^{1}$G. Das and A.C. Wahl, J. Chem. Phys. 44, 87 (1966) $^{2}$A.C. Wahl, J. Chem. Phys. 41, 2600 (1964) $^{3}$H.J. Lipkin, Ann. Phys. (NY) 9, 272 (1960) $^{4}$J.G. Valatin, Phys. Rev. 122, 1012 (1960) $^{5}$Y. Nambu, Phys. Rev. 117, 648 (1960)
Author Institution: Department of Chemistry, Laboratory for Surface Studies, University of Wisconsin-Milwaukee; Johns Hopkins University, Applied Physics Laboratory; Institut f\""{u}r Physikalische und Theoretische Chemie, Universit\""{a}t Regensburg, D-8400 Regensburg, West Germany
Author Institution: Department of Chemistry, Laboratory for Surface Studies, University of Wisconsin-Milwaukee; Johns Hopkins University, Applied Physics Laboratory; Institut f\""{u}r Physikalische und Theoretische Chemie, Universit\""{a}t Regensburg, D-8400 Regensburg, West Germany